PCA_tSNE_UMAP
Jim Costello
7/15/2024
Contents:
Load Metabolomics data and clinial information
The data we will use were collected from individuals with and without Down sydrome. The samples are from blood plasma and metabolomics data were generated for each individual.
# we will use the iris dataset as an illustrative example
data("iris")
iris <- unique(iris) # remove duplicates
iris.mat <- as.matrix(iris[,1:4])
dim(iris)## [1] 149 5colnames(iris)## [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"# read in the raw metabolomics data
x <- getURL("https://raw.githubusercontent.com/DS3-2024/Visualize_Cluster_HTP/main/data/P4C_LCMS_abundance_wide_011722.csv")
mets <- read.csv(text = x, row.names = 1, header = T)
dim(mets)## [1] 419 174row.names(mets)## [1] "HTP0001B2" "HTP0005A3" "HTP0012A2" "HTP0015A4" "HTP0017A4" "HTP0018B3"
## [7] "HTP0019B2" "HTP0022B2" "HTP0023A2" "HTP0025A3" "HTP0026B2" "HTP0034B3"
## [13] "HTP0035B3" "HTP0036A2" "HTP0040B3" "HTP0042B2" "HTP0043B2" "HTP0044B2"
## [19] "HTP0047B2" "HTP0048B2" "HTP0050A3" "HTP0051B2" "HTP0052A2" "HTP0053A2"
## [25] "HTP0054A2" "HTP0055B2" "HTP0057B2" "HTP0058B2" "HTP0059B2" "HTP0061B2"
## [31] "HTP0062B2" "HTP0066A2" "HTP0067B2" "HTP0070A3" "HTP0073A2" "HTP0077B2"
## [37] "HTP0078B2" "HTP0079B2" "HTP0080A2" "HTP0084A2" "HTP0085B2" "HTP0087B2"
## [43] "HTP0090B2" "HTP0092B2" "HTP0095B2" "HTP0096B2" "HTP0098B2" "HTP0100B2"
## [49] "HTP0101A2" "HTP0103A2" "HTP0104B2" "HTP0105B3" "HTP0107A3" "HTP0109A3"
## [55] "HTP0111B2" "HTP0112A3" "HTP0116A2" "HTP0118B" "HTP0119A" "HTP0123A"
## [61] "HTP0125B" "HTP0126B2" "HTP0127B2" "HTP0146B" "HTP0147B" "HTP0148B2"
## [67] "HTP0149B" "HTP0151A" "HTP0198A3" "HTP0202B" "HTP0204A" "HTP0205B"
## [73] "HTP0206B" "HTP0207A4" "HTP0208B" "HTP0211A3" "HTP0213A3" "HTP0214B2"
## [79] "HTP0216B2" "HTP0219A2" "HTP0226A3" "HTP0230A2" "HTP0236A2" "HTP0238A3"
## [85] "HTP0241A2" "HTP0242B3" "HTP0243A3" "HTP0247A2" "HTP0249A2" "HTP0251A2"
## [91] "HTP0254A2" "HTP0259A2" "HTP0261A2" "HTP0262A2" "HTP0263A2" "HTP0277A3"
## [97] "HTP0287B" "HTP0288B" "HTP0289B" "HTP0290B" "HTP0293A" "HTP0294B"
## [103] "HTP0295A" "HTP0296A" "HTP0298A" "HTP0300A" "HTP0301A3" "HTP0303A"
## [109] "HTP0306A" "HTP0307B" "HTP0310A" "HTP0312A2" "HTP0314B" "HTP0315A"
## [115] "HTP0316B" "HTP0318A3" "HTP0319A" "HTP0320A2" "HTP0321A" "HTP0322B"
## [121] "HTP0323A" "HTP0324A2" "HTP0325A" "HTP0326A" "HTP0327A" "HTP0328A"
## [127] "HTP0329A2" "HTP0330A" "HTP0331A" "HTP0332A" "HTP0333A2" "HTP0334A2"
## [133] "HTP0335A2" "HTP0336A" "HTP0337A" "HTP0338B" "HTP0339A" "HTP0340A"
## [139] "HTP0341A" "HTP0342A" "HTP0343B" "HTP0345A" "HTP0346B" "HTP0347B"
## [145] "HTP0348A" "HTP0349B" "HTP0351A" "HTP0352B" "HTP0354A" "HTP0355B"
## [151] "HTP0357A" "HTP0361B2" "HTP0364A" "HTP0367A" "HTP0368A" "HTP0370A"
## [157] "HTP0373A" "HTP0374A" "HTP0375A" "HTP0376B" "HTP0378A" "HTP0379A"
## [163] "HTP0380A" "HTP0381A" "HTP0382A" "HTP0384A" "HTP0385A" "HTP0386A"
## [169] "HTP0387A" "HTP0388A" "HTP0389A" "HTP0390A" "HTP0391A" "HTP0392A"
## [175] "HTP0393A" "HTP0394A" "HTP0395A" "HTP0396A" "HTP0397A" "HTP0398A"
## [181] "HTP0399A2" "HTP0400A" "HTP0401A" "HTP0402A" "HTP0403A" "HTP0404A"
## [187] "HTP0405A" "HTP0406A" "HTP0407A" "HTP0408A" "HTP0409A" "HTP0410A"
## [193] "HTP0411A" "HTP0412A" "HTP0413A" "HTP0414A" "HTP0415A" "HTP0418A"
## [199] "HTP0419A" "HTP0420A" "HTP0421A" "HTP0422A" "HTP0423A" "HTP0424A"
## [205] "HTP0425A" "HTP0426A" "HTP0427A" "HTP0428A" "HTP0429B" "HTP0430A"
## [211] "HTP0431A2" "HTP0432A" "HTP0433A" "HTP0434A" "HTP0435A2" "HTP0436A"
## [217] "HTP0437A" "HTP0438A" "HTP0439A2" "HTP0440A" "HTP0442A2" "HTP0443A2"
## [223] "HTP0444B2" "HTP0445A" "HTP0446A" "HTP0447B2" "HTP0448A" "HTP0449A"
## [229] "HTP0450A" "HTP0451A" "HTP0452A" "HTP0454A" "HTP0455B" "HTP0456A"
## [235] "HTP0457B" "HTP0458A" "HTP0459A" "HTP0460A" "HTP0461A" "HTP0462A"
## [241] "HTP0463A" "HTP0464A" "HTP0465A" "HTP0466B" "HTP0467A" "HTP0468A2"
## [247] "HTP0469A" "HTP0470A" "HTP0471A" "HTP0472A" "HTP0473A" "HTP0474A"
## [253] "HTP0475A" "HTP0476A" "HTP0477A" "HTP0478A" "HTP0479A" "HTP0480A"
## [259] "HTP0482A" "HTP0484A" "HTP0485A" "HTP0487A" "HTP0488A" "HTP0491A"
## [265] "HTP0492B" "HTP0493B" "HTP0494A" "HTP0495B" "HTP0497B" "HTP0498B"
## [271] "HTP0501A" "HTP0502B" "HTP0506B" "HTP0507A" "HTP0508B2" "HTP0510A"
## [277] "HTP0512A" "HTP0514A" "HTP0515A" "HTP0516A" "HTP0517A" "HTP0519A"
## [283] "HTP0520B" "HTP0523B" "HTP0524B" "HTP0525A" "HTP0527B" "HTP0530A"
## [289] "HTP0531A" "HTP0534A" "HTP0535A" "HTP0537A" "HTP0538A" "HTP0539A"
## [295] "HTP0540A" "HTP0541A" "HTP0542A" "HTP0543A" "HTP0544A" "HTP0545A"
## [301] "HTP0546A" "HTP0547A" "HTP0548A" "HTP0549A" "HTP0550A" "HTP0551B"
## [307] "HTP0552A" "HTP0553A" "HTP0554A" "HTP0555B" "HTP0556A" "HTP0557B"
## [313] "HTP0559B" "HTP0560A" "HTP0561A" "HTP0563A" "HTP0564A" "HTP0565A"
## [319] "HTP0566A" "HTP0567B" "HTP0568A" "HTP0569A" "HTP0570A" "HTP0571A"
## [325] "HTP0572A" "HTP0573B" "HTP0574A" "HTP0575A" "HTP0576B" "HTP0577A"
## [331] "HTP0578A" "HTP0580A" "HTP0581A" "HTP0582B" "HTP0583A" "HTP0584A"
## [337] "HTP0585A" "HTP0586A" "HTP0587A" "HTP0588A" "HTP0589A" "HTP0590A"
## [343] "HTP0591A" "HTP0592A" "HTP0593A" "HTP0594A" "HTP0595B" "HTP0596A"
## [349] "HTP0597A" "HTP0598A" "HTP0599A" "HTP0600A" "HTP0602A" "HTP0603A"
## [355] "HTP0604A" "HTP0605A" "HTP0607A" "HTP0608A" "HTP0609A" "HTP0610A"
## [361] "HTP0611A" "HTP0612A" "HTP0613A" "HTP0615B" "HTP0616A" "HTP0617A"
## [367] "HTP0618A" "HTP0619A" "HTP0620A" "HTP0621A" "HTP0622A" "HTP0623A"
## [373] "HTP0624A" "HTP0625A" "HTP0626A" "HTP0627A" "HTP0628B" "HTP0629A"
## [379] "HTP0630A" "HTP0631A" "HTP0632A" "HTP0633A" "HTP0634A" "HTP0637A"
## [385] "HTP0638A" "HTP0639A" "HTP0641A" "HTP0642A" "HTP0643A" "HTP0644A"
## [391] "HTP0645A" "HTP0646A" "HTP0647A" "HTP0648B" "HTP0649B" "HTP0650A"
## [397] "HTP0651A" "HTP0652A" "HTP0653B" "HTP0654A" "HTP0655B" "HTP0657A"
## [403] "HTP0658A" "HTP0659A" "HTP0660A" "HTP0661A" "HTP0662A" "HTP0663A"
## [409] "HTP0664A" "HTP0665A" "HTP0666A" "HTP0667A" "HTP0668A" "HTP0669B"
## [415] "HTP0672A" "HTP0676A" "HTP0677B" "HTP0706A" "HTP0708A"colnames(mets)## [1] "X.15Z..Tetracosenoic.acid"
## [2] "X.5.L.Glutamyl..L.glutamine"
## [3] "X1.4.beta.D.Xylan"
## [4] "X10.S.17.S..DiHDHA.protectin.D1"
## [5] "X11.HETE"
## [6] "X12.S..HETE"
## [7] "X15.S..HETE"
## [8] "X2.Oxoglutaramate"
## [9] "X2.Oxoglutarate"
## [10] "X3..5..Cyclic.IMP"
## [11] "X3.Methyleneoxindole"
## [12] "X4.Acetamidobutanoate"
## [13] "X4.Pyridoxate"
## [14] "X5..Phosphoribosyl.N.formylglycinamide"
## [15] "X5.6.Dihydrothymine"
## [16] "X5.Guanidino.2.oxopentanoate"
## [17] "X5.Hydroxyindoleacetate"
## [18] "X5.Hydroxyisourate"
## [19] "X5.Oxoproline"
## [20] "X5.S..HETE"
## [21] "acetyl.carnitine"
## [22] "Acetylcholine"
## [23] "acyl.C12..O.dodecanoyl.carnitine."
## [24] "acyl.C12.1..O.dodecenoyl.carnitine."
## [25] "acyl.C14..O.tetradecanoyl.L.carnitine."
## [26] "acyl.C14.1..Tetradecenoyl.Carnitine."
## [27] "acyl.C16..L.Palmitoylcarnitine."
## [28] "acyl.C16.1..Hexadecenoyl.carnitine."
## [29] "acyl.C18..Octadecanoyl.L.carnitine."
## [30] "acyl.C18.1..O.octadecenoyl.L.carnitine."
## [31] "acyl.C18.2"
## [32] "acyl.C4.DC"
## [33] "acyl.C5"
## [34] "acyl.C5.OH"
## [35] "acyl.C5.1"
## [36] "Adenine"
## [37] "Adenosine"
## [38] "Alanine"
## [39] "Allantoate"
## [40] "AMP"
## [41] "Anthranilate"
## [42] "Arginine"
## [43] "Ascorbate"
## [44] "Asparagine"
## [45] "Aspartate"
## [46] "butanoyl.l.carnitine"
## [47] "Chenodeoxycholic.acid"
## [48] "Cholic.acid"
## [49] "Choline"
## [50] "Citrate"
## [51] "Creatine"
## [52] "Creatinine"
## [53] "Cys.Gly"
## [54] "Cysteine"
## [55] "Cystine"
## [56] "D.Arabitol"
## [57] "D.Glucono.1.5.lactone.6.phosphate"
## [58] "D.Glucose"
## [59] "D.Rhamnose"
## [60] "D.Ribose"
## [61] "Decanoic.acid..caprate."
## [62] "Dehydroascorbate"
## [63] "Deoxycholic.acid"
## [64] "DiHOME"
## [65] "Dihomo.g.Linolenic.acid.eicosatrienoic.acid"
## [66] "Dimethylglycine"
## [67] "Diphosphate"
## [68] "Docosahexaenoic.acid"
## [69] "Docosapentaenoic.acid"
## [70] "Dodecanedioic.acid"
## [71] "Dodecanoic.acid"
## [72] "Dopamine"
## [73] "Ectoine"
## [74] "EpOME.HODE"
## [75] "Fumarate"
## [76] "gamma.Glutamyl.Se.methylselenocysteine"
## [77] "gamma.L.Glutamyl.D.alanine"
## [78] "Glutamate"
## [79] "Glutamine"
## [80] "Glycerol.3.phosphate"
## [81] "Glycine"
## [82] "Glycochenodeoxycholic.acid"
## [83] "Glycocholic.acid"
## [84] "Guanidinoacetate"
## [85] "Guanine"
## [86] "HEPE.oxoETE"
## [87] "Heptanoic.acid"
## [88] "Hexadecanoic.acid"
## [89] "Hexadecenoic.acid"
## [90] "Hexanoic.acid..caproate."
## [91] "hexanoyl.L.carnitine"
## [92] "Hexose.phosphate"
## [93] "Histidine"
## [94] "HOTrE.oxoODE"
## [95] "Hypoxanthine"
## [96] "Icosapentaenoic.acid"
## [97] "Icosatetraenoic.acid"
## [98] "IDP"
## [99] "Indole"
## [100] "Indole.3.acetaldehyde"
## [101] "Indole.3.acetate"
## [102] "kynurenine"
## [103] "L.Adrenaline"
## [104] "L.Arabinose"
## [105] "L.Carnitine"
## [106] "L.Citrulline"
## [107] "L.Methionine.S.oxide"
## [108] "L.octanoylcarnitine"
## [109] "Lactate"
## [110] "Leucine.isoleucine"
## [111] "Leukotriene.B4.PGA1.PGB1"
## [112] "Linoleate"
## [113] "LPA_16.0"
## [114] "LPA_16.1"
## [115] "LPA_18.2"
## [116] "LPA_20.4"
## [117] "Lysine"
## [118] "Lysophosphatidic.Acid"
## [119] "Lysophosphatidylinositol"
## [120] "Malate"
## [121] "Maltose"
## [122] "Mannitol"
## [123] "Methionine"
## [124] "N.Acetylneuraminate"
## [125] "N.Acetylornithine"
## [126] "N.formyl.kynurenine"
## [127] "Nonanoic.acid..pelargonate."
## [128] "O.Decanoyl.L.carnitine"
## [129] "O.Decenoyl.L.carnitine"
## [130] "Octadecanoic.acid"
## [131] "Octadecatrienoic.acid"
## [132] "Octadecenoic.acid..Oleic.acid."
## [133] "Octanoic.acid..caprylate."
## [134] "octenoyl.l.carnitine"
## [135] "Ornithine"
## [136] "Oxaloacetate"
## [137] "Pantothenate"
## [138] "Phenylalanine"
## [139] "Phosphate"
## [140] "Picolinic.acid"
## [141] "Proline"
## [142] "propionyl.carnitine"
## [143] "Prostaglandin.A2.B2.J2"
## [144] "Prostaglandin.A3.B3"
## [145] "Pyridoxal"
## [146] "Pyridoxamine.5..phosphate"
## [147] "Pyruvate"
## [148] "quinolinic.acid"
## [149] "Resolvin.D1.D2"
## [150] "S.Adenosyl.L.homocysteine"
## [151] "Serine"
## [152] "Sphinganine.1.phosphate"
## [153] "Sphingosine"
## [154] "Sphingosine.1.phosphate"
## [155] "Stearidonic.acid"
## [156] "Succinate"
## [157] "Taurine"
## [158] "Taurochenodeoxycholic.acid"
## [159] "Taurocholic.acid"
## [160] "Taurodeoxycholic.acid"
## [161] "Taurolithocholic.acid"
## [162] "Tauroursodeoxycholic.acid"
## [163] "Tetradecanoic.acid"
## [164] "Threonine"
## [165] "Thymidine"
## [166] "trans.4.Hydroxy.L.proline"
## [167] "Tryptophan"
## [168] "Tyrosine"
## [169] "UDP"
## [170] "UMP"
## [171] "Urate"
## [172] "Ursodeoxycholic.acid"
## [173] "Valine"
## [174] "Xanthine"#read in the metadata
x <- getURL("https://raw.githubusercontent.com/DS3-2024/Visualize_Cluster_HTP/main/data/P4C_metadata_011722.csv")
info <- read.csv(text = x, row.names = 1, header = T)
dim(info)## [1] 587 21colnames(info)## [1] "RecordID" "Sex"
## [3] "Karyotype" "Event_name"
## [5] "LabID" "Age_at_visit"
## [7] "BMI" "Sample_source"
## [9] "Anxiety" "Any.autoimmune.skin.condition"
## [11] "Any.congenital.heart.defect" "Any.hearing.loss.condition"
## [13] "Any.hypothyroidism" "Any.seizure.history"
## [15] "Any.sleep.apnea" "Asthma.reactive.airway.disease"
## [17] "Celiac.disease" "Depression"
## [19] "Frequent.Recurrent.pneumonia" "Obesity"
## [21] "Recurrent.otitis.media"# make sure the patient order matches in both the meta data and the metabolimcs data
patients <- intersect(row.names(mets), row.names(info))
length(patients)## [1] 419mets <- mets[patients,]
info <- info[patients,]
mets <- mets[order(info$Karyotype),]
info <- info[order(info$Karyotype),]
# remove the batch effect of sample source where the samples were collected
mets <- 2^t((removeBatchEffect(t(log2(mets)), batch=info$Sample_source)))
info$order <- seq(1,nrow(info))
info$Karyotype <- as.factor(info$Karyotype)
mets.info <- cbind(log2(mets), info)Principal Component Analysis
We will use PCA to plot the data and explore sample information. The examples used here is taken from Statquest. Please refer to the PCA video.
We will also be using this image to illustrate the regression line
fit 
# 1D
ids <- grep("T21",mets.info$Karyotype)
plot(mets.info$Prostaglandin.A2.B2.J2[ids],rep(0,length(mets.info$Prostaglandin.A2.B2.J2[ids])), pch=20, ylab="", xlab="Prostaglandin.A2.B2.J2 expression", cex=1, col="lightseagreen")
ids <- grep("Control",mets.info$Karyotype)
points(mets.info$Prostaglandin.A2.B2.J2[ids],rep(0.05,length(mets.info$Prostaglandin.A2.B2.J2[ids])), pch=20, col="salmon", cex=1)
legend(10, 1, fill=c("lightseagreen", "salmon"), legend=c("T21", "Control"))
ggplot(mets.info, aes(x=Karyotype, y=Prostaglandin.A2.B2.J2, fill=Karyotype)) + geom_boxplot() + geom_jitter() + theme_bw()
# 2D
ggplot(mets.info, aes(x=Hypoxanthine, y=Prostaglandin.A2.B2.J2, color=Karyotype)) + geom_point() + theme_bw()
# lets look at a simplified example
Met1 <- c(10,11,8,3,1,3)
Met2 <- c(5,4,5,3,3,1)
plot(Met1, Met2, pch =19)
# find the mean of M1 and M2
plot(Met1, Met2, pch =19)
points(mean(Met1), mean(Met2), col="purple", pch=19, cex=3) 
# center the data and plot
Met1 = Met1 - mean(Met1)
Met2 = Met2 - mean(Met2)
plot(Met1, Met2, pch =19)
segments(0,-10,0,20, col="grey", lty=2)
segments(-10,0,20,0, col="grey", lty=2)
# add a regression line
plot(Met1, Met2, pch =19)
segments(0,-10,0,20, col="grey", lty=2)
segments(-10,0,20,0, col="grey", lty=2)
abline(lm(Met2~Met1))
segments(0,0,4,0, col="red", lwd=2)
segments(4,1,4,0, col="red", lwd=2)
# back to the HTP data
# find the mean of the X and Y directions
ggplot(mets.info, aes(x=Hypoxanthine, y=Prostaglandin.A2.B2.J2)) + geom_point() + theme_bw() +
geom_point(aes(x=mean(mets.info$Hypoxanthine),y=mean(mets.info$Prostaglandin.A2.B2.J2)), colour="purple", size=5)## Warning: Use of `mets.info$Hypoxanthine` is discouraged.
## ℹ Use `Hypoxanthine` instead.## Warning: Use of `mets.info$Prostaglandin.A2.B2.J2` is discouraged.
## ℹ Use `Prostaglandin.A2.B2.J2` instead.## Warning in geom_point(aes(x = mean(mets.info$Hypoxanthine), y = mean(mets.info$Prostaglandin.A2.B2.J2)), : All aesthetics have length 1, but the data has 419 rows.
## ℹ Please consider using `annotate()` or provide this layer with data containing
## a single row.
# center the data and plot
mets.info$Hypoxanthine.standard <- mets.info$Hypoxanthine - mean(mets.info$Hypoxanthine)
mets.info$Prostaglandin.A2.B2.J2.standard <- mets.info$Prostaglandin.A2.B2.J2 - mean(mets.info$Prostaglandin.A2.B2.J2)
ggplot(mets.info, aes(x=Hypoxanthine.standard, y=Prostaglandin.A2.B2.J2.standard)) + geom_point() + theme_bw()
# add a regression line
ggplot(mets.info, aes(x=Hypoxanthine.standard, y=Prostaglandin.A2.B2.J2.standard)) + geom_point() + theme_bw() + geom_smooth(method='lm',se=F) + geom_point(aes(x=0,y=0), colour="red")## Warning in geom_point(aes(x = 0, y = 0), colour = "red"): All aesthetics have length 1, but the data has 419 rows.
## ℹ Please consider using `annotate()` or provide this layer with data containing
## a single row.
# note in the prcomp implementation of PCA,
# x = PCs
# rotation = loadings
# sdev^2 = eigenvalues
#Iris data
pca <- prcomp(na.omit(iris.mat), scale=T)
autoplot(pca, data=iris, col='Species')
pca$rotation #display the loadings (named rotation in the prcomp data structure)## PC1 PC2 PC3 PC4
## Sepal.Length 0.5220620 -0.37334080 0.7203991 0.2628555
## Sepal.Width -0.2676921 -0.92485914 -0.2402154 -0.1235842
## Petal.Length 0.5803119 -0.02431115 -0.1405854 -0.8017998
## Petal.Width 0.5648277 -0.06827292 -0.6352617 0.5222557get_eigenvalue(pca)## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 2.91964087 72.9910218 72.99102
## Dim.2 0.91432690 22.8581724 95.84919
## Dim.3 0.14524258 3.6310646 99.48026
## Dim.4 0.02078965 0.5197411 100.00000fviz_pca_var(pca,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
#HTP data
pca <- prcomp(na.omit(mets), scale=T)
autoplot(pca, data=info, col='Karyotype')
autoplot(pca, data=info, col='Sample_source')
# remove outlier samples
hist(pca$x[,1], main ="PC1")
sort(pca$x[,1])## HTP0378A HTP0561A HTP0549A HTP0467A HTP0388A HTP0336A
## -9.45231329 -9.43089445 -8.95691066 -8.56379238 -8.26244962 -8.12758694
## HTP0556A HTP0035B3 HTP0357A HTP0243A3 HTP0545A HTP0331A
## -8.07235771 -7.78774025 -7.39167744 -7.33834927 -7.05604314 -7.01753433
## HTP0573B HTP0087B2 HTP0116A2 HTP0249A2 HTP0226A3 HTP0530A
## -6.96902574 -6.92198497 -6.84419532 -6.71153550 -6.65555618 -6.38150174
## HTP0457B HTP0026B2 HTP0464A HTP0315A HTP0577A HTP0547A
## -6.29000484 -6.24484713 -6.18076934 -6.17022779 -6.08716521 -5.97439384
## HTP0295A HTP0296A HTP0609A HTP0211A3 HTP0219A2 HTP0300A
## -5.92240655 -5.90097381 -5.80035071 -5.46584207 -5.39695345 -5.35184620
## HTP0015A4 HTP0105B3 HTP0659A HTP0598A HTP0251A2 HTP0572A
## -5.14371773 -5.13666464 -5.12693853 -5.11191334 -5.00495986 -4.98500726
## HTP0563A HTP0649B HTP0335A2 HTP0434A HTP0277A3 HTP0550A
## -4.88441199 -4.86726583 -4.77222842 -4.73983468 -4.73053209 -4.67116259
## HTP0050A3 HTP0663A HTP0569A HTP0668A HTP0052A2 HTP0040B3
## -4.66496085 -4.65680951 -4.65290610 -4.63500448 -4.63331644 -4.62356407
## HTP0404A HTP0622A HTP0123A HTP0399A2 HTP0484A HTP0616A
## -4.61688961 -4.60125127 -4.60019628 -4.56419010 -4.48058543 -4.47802469
## HTP0512A HTP0439A2 HTP0409A HTP0044B2 HTP0394A HTP0553A
## -4.44592032 -4.34502161 -4.29783706 -4.29235373 -4.26612327 -4.14024148
## HTP0605A HTP0669B HTP0306A HTP0325A HTP0207A4 HTP0589A
## -4.13111294 -4.13089470 -4.10278883 -4.08273918 -4.01286557 -3.99321139
## HTP0073A2 HTP0022B2 HTP0147B HTP0054A2 HTP0537A HTP0654A
## -3.89744022 -3.82304576 -3.77290899 -3.68454990 -3.64699215 -3.61249581
## HTP0351A HTP0506B HTP0619A HTP0585A HTP0566A HTP0413A
## -3.60398334 -3.60195316 -3.57545873 -3.57522995 -3.54878317 -3.53861756
## HTP0442A2 HTP0414A HTP0440A HTP0329A2 HTP0396A HTP0107A3
## -3.53135576 -3.49583482 -3.48496675 -3.42882274 -3.41924028 -3.41594221
## HTP0307B HTP0059B2 HTP0392A HTP0151A HTP0407A HTP0610A
## -3.40092351 -3.38059301 -3.34712147 -3.31298862 -3.27853373 -3.24286956
## HTP0571A HTP0078B2 HTP0070A3 HTP0321A HTP0018B3 HTP0084A2
## -3.20784983 -3.19465773 -3.13236649 -3.11923195 -3.11503758 -2.92045509
## HTP0202B HTP0401A HTP0523B HTP0379A HTP0312A2 HTP0428A
## -2.89930509 -2.86857682 -2.85537356 -2.81930417 -2.81135628 -2.76801536
## HTP0445A HTP0567B HTP0386A HTP0429B HTP0348A HTP0586A
## -2.75857726 -2.74765567 -2.72260896 -2.69902398 -2.65616351 -2.62773769
## HTP0664A HTP0001B2 HTP0482A HTP0389A HTP0241A2 HTP0517A
## -2.59510420 -2.56225653 -2.55379981 -2.53560720 -2.52256135 -2.51854259
## HTP0324A2 HTP0303A HTP0557B HTP0639A HTP0582B HTP0495B
## -2.51570564 -2.51049193 -2.47909933 -2.47465294 -2.46101064 -2.45721588
## HTP0263A2 HTP0665A HTP0564A HTP0418A HTP0469A HTP0119A
## -2.44098237 -2.43774740 -2.43534023 -2.29983569 -2.28979908 -2.28886769
## HTP0017A4 HTP0109A3 HTP0148B2 HTP0559B HTP0347B HTP0254A2
## -2.24805294 -2.23964576 -2.22130761 -2.21494693 -2.18597054 -2.18224787
## HTP0259A2 HTP0036A2 HTP0641A HTP0570A HTP0592A HTP0661A
## -2.17892269 -2.14456379 -2.12721997 -2.11974981 -2.11045510 -2.08309722
## HTP0552A HTP0652A HTP0479A HTP0334A2 HTP0584A HTP0408A
## -2.04816718 -2.00323676 -1.98844968 -1.96640957 -1.95124012 -1.91148223
## HTP0516A HTP0326A HTP0242B3 HTP0548A HTP0034B3 HTP0376B
## -1.90683102 -1.89295717 -1.84673786 -1.81820028 -1.75851698 -1.75809092
## HTP0455B HTP0531A HTP0627A HTP0433A HTP0419A HTP0236A2
## -1.75775028 -1.74352619 -1.72530504 -1.68454341 -1.64110839 -1.59125919
## HTP0574A HTP0554A HTP0460A HTP0651A HTP0043B2 HTP0337A
## -1.58070319 -1.55650559 -1.55546543 -1.55146462 -1.52420495 -1.46372157
## HTP0103A2 HTP0019B2 HTP0323A HTP0332A HTP0576B HTP0343B
## -1.43065053 -1.40923277 -1.40452849 -1.39946060 -1.34291138 -1.32589629
## HTP0205B HTP0294B HTP0101A2 HTP0588A HTP0637A HTP0676A
## -1.28851159 -1.28525815 -1.27623333 -1.25177347 -1.25050983 -1.23438158
## HTP0477A HTP0112A3 HTP0370A HTP0422A HTP0316B HTP0621A
## -1.20621742 -1.11991513 -1.10908515 -1.10445041 -1.10387767 -1.09794574
## HTP0427A HTP0594A HTP0288B HTP0345A HTP0480A HTP0487A
## -1.08719763 -1.04825989 -1.01761080 -0.99943763 -0.99526275 -0.99454138
## HTP0406A HTP0476A HTP0023A2 HTP0540A HTP0638A HTP0096B2
## -0.93446088 -0.92468697 -0.88620511 -0.86209968 -0.84268004 -0.83343120
## HTP0149B HTP0612A HTP0214B2 HTP0341A HTP0400A HTP0100B2
## -0.82713027 -0.79980099 -0.79605706 -0.79439494 -0.76675535 -0.75407006
## HTP0330A HTP0432A HTP0425A HTP0575A HTP0613A HTP0602A
## -0.75316030 -0.74039554 -0.73853296 -0.73564629 -0.68612973 -0.68103913
## HTP0055B2 HTP0534A HTP0471A HTP0340A HTP0118B HTP0525A
## -0.64834747 -0.62988362 -0.60192790 -0.59757722 -0.58569356 -0.57503685
## HTP0527B HTP0051B2 HTP0403A HTP0624A HTP0067B2 HTP0485A
## -0.54818056 -0.52754352 -0.52098902 -0.48999323 -0.47434952 -0.47267320
## HTP0591A HTP0643A HTP0398A HTP0430A HTP0538A HTP0053A2
## -0.46254279 -0.38316612 -0.37868498 -0.34347475 -0.33041914 -0.32410168
## HTP0230A2 HTP0402A HTP0607A HTP0587A HTP0374A HTP0544A
## -0.31766948 -0.31439263 -0.25982378 -0.25285375 -0.18652073 -0.09765263
## HTP0339A HTP0111B2 HTP0390A HTP0653B HTP0058B2 HTP0435A2
## -0.09126631 -0.07945610 -0.05792800 -0.05384159 -0.02664515 -0.01577486
## HTP0314B HTP0436A HTP0328A HTP0420A HTP0535A HTP0298A
## 0.01995694 0.03087348 0.04166979 0.06308144 0.06821869 0.08999450
## HTP0642A HTP0437A HTP0603A HTP0565A HTP0618A HTP0644A
## 0.10363101 0.13011771 0.15292021 0.20018315 0.23001954 0.23691402
## HTP0127B2 HTP0206B HTP0301A3 HTP0508B2 HTP0238A3 HTP0578A
## 0.29495125 0.29739942 0.30184844 0.30980492 0.31258726 0.34637577
## HTP0491A HTP0104B2 HTP0451A HTP0630A HTP0327A HTP0393A
## 0.34854551 0.36022592 0.36901618 0.38122240 0.38955712 0.40365139
## HTP0475A HTP0658A HTP0391A HTP0125B HTP0519A HTP0085B2
## 0.44292110 0.45003876 0.50101866 0.51929552 0.54223412 0.54242697
## HTP0410A HTP0361B2 HTP0423A HTP0593A HTP0667A HTP0660A
## 0.54845247 0.56324174 0.63058255 0.65535612 0.66815425 0.67821123
## HTP0450A HTP0384A HTP0411A HTP0604A HTP0364A HTP0287B
## 0.70376361 0.72894429 0.73263754 0.79628683 0.80861881 0.81599587
## HTP0092B2 HTP0666A HTP0657A HTP0349B HTP0465A HTP0520B
## 0.84853834 0.86948449 0.88298664 0.88913478 0.89273872 0.92563891
## HTP0098B2 HTP0611A HTP0650A HTP0061B2 HTP0352B HTP0623A
## 0.96769924 0.97109566 1.02064631 1.03967667 1.04581576 1.05251147
## HTP0608A HTP0662A HTP0354A HTP0461A HTP0625A HTP0319A
## 1.09373138 1.11228125 1.20499925 1.20870270 1.22158558 1.28346437
## HTP0048B2 HTP0025A3 HTP0590A HTP0126B2 HTP0342A HTP0066A2
## 1.32551879 1.33396822 1.38646417 1.42932646 1.43742009 1.49174987
## HTP0456A HTP0080A2 HTP0095B2 HTP0213A3 HTP0424A HTP0005A3
## 1.54530395 1.60236137 1.60592690 1.62753641 1.62761640 1.69679816
## HTP0492B HTP0405A HTP0333A2 HTP0468A2 HTP0090B2 HTP0387A
## 1.75043068 1.75449463 1.78042760 1.78707064 1.81711321 1.88350102
## HTP0382A HTP0497B HTP0426A HTP0446A HTP0079B2 HTP0462A
## 1.91405480 1.92559660 1.92920669 1.95512458 1.95840767 1.98138185
## HTP0708A HTP0581A HTP0057B2 HTP0447B2 HTP0510A HTP0472A
## 2.00688001 2.02370482 2.06626497 2.13682062 2.16443887 2.17850360
## HTP0473A HTP0320A2 HTP0452A HTP0431A2 HTP0515A HTP0454A
## 2.21598587 2.24573600 2.30176253 2.30623748 2.36911121 2.37831310
## HTP0599A HTP0289B HTP0595B HTP0617A HTP0346B HTP0466B
## 2.41236974 2.42579438 2.43494407 2.49180197 2.54140900 2.62088226
## HTP0632A HTP0560A HTP0421A HTP0047B2 HTP0634A HTP0381A
## 2.64769510 2.76147873 2.95348092 2.95546895 3.07004956 3.08093601
## HTP0380A HTP0543A HTP0463A HTP0501A HTP0459A HTP0012A2
## 3.10317496 3.11083133 3.13132675 3.15691751 3.17798667 3.21152691
## HTP0204A HTP0458A HTP0488A HTP0438A HTP0474A HTP0502B
## 3.22487639 3.24405016 3.26430011 3.31658692 3.46723232 3.52376816
## HTP0494A HTP0443A2 HTP0706A HTP0672A HTP0583A HTP0216B2
## 3.56561560 3.78024966 3.91704112 3.92182984 3.93954234 3.95246190
## HTP0062B2 HTP0647A HTP0539A HTP0478A HTP0397A HTP0412A
## 3.98192042 4.04785526 4.06729105 4.16899341 4.19171501 4.24802155
## HTP0395A HTP0514A HTP0580A HTP0546A HTP0385A HTP0542A
## 4.30520520 4.32180884 4.40498022 4.42076596 4.44241101 4.46680236
## HTP0448A HTP0262A2 HTP0646A HTP0367A HTP0444B2 HTP0633A
## 4.51574297 4.54104473 4.64802430 4.70543086 4.82461870 4.88651189
## HTP0555B HTP0208B HTP0355B HTP0375A HTP0368A HTP0626A
## 4.89717903 4.95544348 4.96342155 5.01319081 5.07597029 5.13792464
## HTP0261A2 HTP0290B HTP0631A HTP0629A HTP0645A HTP0551B
## 5.23871385 5.34392058 5.57489848 5.62549060 5.72452691 5.84094282
## HTP0600A HTP0470A HTP0449A HTP0318A3 HTP0677B HTP0655B
## 5.90156552 6.06904551 6.26773986 6.42324259 6.55812703 7.01236448
## HTP0597A HTP0077B2 HTP0524B HTP0373A HTP0615B HTP0620A
## 7.03108216 7.25306884 7.30972716 7.54452671 7.77829543 8.91447993
## HTP0648B HTP0042B2 HTP0322B HTP0415A HTP0507A HTP0628B
## 9.03609172 9.15597370 9.20316503 9.96060302 10.22714064 10.57801003
## HTP0198A3 HTP0293A HTP0310A HTP0146B HTP0493B HTP0338B
## 11.06122111 11.09098080 11.29508705 11.40109323 12.53692307 12.79348372
## HTP0498B HTP0247A2 HTP0596A HTP0568A HTP0541A
## 13.35725235 15.36261472 19.19796064 34.19194982 42.56208877row.names(mets)[pca$x[,1] > 15]## [1] "HTP0247A2" "HTP0541A" "HTP0568A" "HTP0596A"mets <- mets[pca$x[,1] < 15,]
info <- info[pca$x[,1] < 15,]
mets.info <- cbind(mets, info)
dim(mets)## [1] 415 174pca <- prcomp(na.omit(mets), scale=T)
autoplot(pca, data=info, col='Karyotype')
autoplot(pca, data=info, col='Sample_source')
autoplot(pca, data=info, col='Age_at_visit')
# scree plot
var_explained = cbind(PC=seq(1, length(pca$sdev)), var=100*(pca$sdev^2 / sum(pca$sdev^2)))
ggplot(var_explained, aes(x=PC, y=var)) + geom_line() + xlab("Principal Component") + theme_bw() +
ylab("Variance Explained (%)") + ggtitle("Scree Plot") + xlim(1,20)## Warning: Removed 154 rows containing missing values or values outside the scale range
## (`geom_line()`).
t-distributed stochastic neighbor embedding
We will use tSNE to plot the data and explore sample information
# tSNE is stochastic so it will produce different results based on the random seed. To get the same results, you will need to fix the seed
set.seed(48673)
# theta is parameter that balances speed and accuracy. theta=0 is the exact tSNE calculation
# perplexity is the value that balances density of the cluster size
#Iris data
tsne <- Rtsne(iris.mat, pca=F, verbose=T, perplexity=30, theta=0)## Read the 149 x 4 data matrix successfully!
## Using no_dims = 2, perplexity = 30.000000, and theta = 0.000000
## Computing input similarities...
## Symmetrizing...
## Done in 0.00 seconds!
## Learning embedding...
## Iteration 50: error is 43.428456 (50 iterations in 0.01 seconds)
## Iteration 100: error is 47.122936 (50 iterations in 0.01 seconds)
## Iteration 150: error is 46.191149 (50 iterations in 0.01 seconds)
## Iteration 200: error is 43.840578 (50 iterations in 0.01 seconds)
## Iteration 250: error is 44.242374 (50 iterations in 0.01 seconds)
## Iteration 300: error is 0.464825 (50 iterations in 0.01 seconds)
## Iteration 350: error is 0.149986 (50 iterations in 0.01 seconds)
## Iteration 400: error is 0.137901 (50 iterations in 0.01 seconds)
## Iteration 450: error is 0.132383 (50 iterations in 0.01 seconds)
## Iteration 500: error is 0.130166 (50 iterations in 0.01 seconds)
## Iteration 550: error is 0.128999 (50 iterations in 0.01 seconds)
## Iteration 600: error is 0.128274 (50 iterations in 0.01 seconds)
## Iteration 650: error is 0.127771 (50 iterations in 0.01 seconds)
## Iteration 700: error is 0.127393 (50 iterations in 0.01 seconds)
## Iteration 750: error is 0.127103 (50 iterations in 0.01 seconds)
## Iteration 800: error is 0.126862 (50 iterations in 0.01 seconds)
## Iteration 850: error is 0.126670 (50 iterations in 0.01 seconds)
## Iteration 900: error is 0.126505 (50 iterations in 0.01 seconds)
## Iteration 950: error is 0.126362 (50 iterations in 0.01 seconds)
## Iteration 1000: error is 0.126241 (50 iterations in 0.01 seconds)
## Fitting performed in 0.13 seconds.iris.info.tsne <- cbind(tsne$Y, iris)
colnames(iris.info.tsne)[1] <- "tsne1"
colnames(iris.info.tsne)[2] <- "tsne2"
ggplot(iris.info.tsne, aes(x=tsne1, y=tsne2, color=Species)) + geom_point() + theme_bw() 
#HTP data
tsne <- Rtsne(mets, pca=F, verbose=T, perplexity=30, theta=0)## Read the 415 x 174 data matrix successfully!
## Using no_dims = 2, perplexity = 30.000000, and theta = 0.000000
## Computing input similarities...
## Symmetrizing...
## Done in 0.02 seconds!
## Learning embedding...
## Iteration 50: error is 55.599908 (50 iterations in 0.05 seconds)
## Iteration 100: error is 55.052849 (50 iterations in 0.05 seconds)
## Iteration 150: error is 55.045881 (50 iterations in 0.05 seconds)
## Iteration 200: error is 55.050591 (50 iterations in 0.05 seconds)
## Iteration 250: error is 55.049018 (50 iterations in 0.05 seconds)
## Iteration 300: error is 0.753257 (50 iterations in 0.05 seconds)
## Iteration 350: error is 0.698318 (50 iterations in 0.05 seconds)
## Iteration 400: error is 0.685135 (50 iterations in 0.05 seconds)
## Iteration 450: error is 0.680085 (50 iterations in 0.05 seconds)
## Iteration 500: error is 0.678387 (50 iterations in 0.05 seconds)
## Iteration 550: error is 0.677656 (50 iterations in 0.05 seconds)
## Iteration 600: error is 0.677346 (50 iterations in 0.05 seconds)
## Iteration 650: error is 0.677217 (50 iterations in 0.05 seconds)
## Iteration 700: error is 0.677162 (50 iterations in 0.05 seconds)
## Iteration 750: error is 0.677137 (50 iterations in 0.05 seconds)
## Iteration 800: error is 0.677126 (50 iterations in 0.05 seconds)
## Iteration 850: error is 0.677121 (50 iterations in 0.05 seconds)
## Iteration 900: error is 0.677118 (50 iterations in 0.05 seconds)
## Iteration 950: error is 0.677116 (50 iterations in 0.05 seconds)
## Iteration 1000: error is 0.677116 (50 iterations in 0.05 seconds)
## Fitting performed in 0.97 seconds.mets.info.tsne <- cbind(tsne$Y, mets.info)
colnames(mets.info.tsne)[1] <- "tsne1"
colnames(mets.info.tsne)[2] <- "tsne2"
ggplot(mets.info.tsne, aes(x=tsne1, y=tsne2, color=Karyotype)) + geom_point() + theme_bw() 
ggplot(mets.info.tsne, aes(x=tsne1, y=tsne2, color=Sex)) + geom_point() + theme_bw() 
ggplot(mets.info.tsne, aes(x=tsne1, y=tsne2, color=Sample_source)) + geom_point() + theme_bw() 
# playing with perplexity
tsne <- Rtsne(mets, pca=F, verbose=T, perplexity=5, theta=0)## Read the 415 x 174 data matrix successfully!
## Using no_dims = 2, perplexity = 5.000000, and theta = 0.000000
## Computing input similarities...
## Symmetrizing...
## Done in 0.02 seconds!
## Learning embedding...
## Iteration 50: error is 72.563005 (50 iterations in 0.05 seconds)
## Iteration 100: error is 69.723166 (50 iterations in 0.05 seconds)
## Iteration 150: error is 69.565391 (50 iterations in 0.05 seconds)
## Iteration 200: error is 69.657449 (50 iterations in 0.05 seconds)
## Iteration 250: error is 69.423648 (50 iterations in 0.05 seconds)
## Iteration 300: error is 1.213984 (50 iterations in 0.05 seconds)
## Iteration 350: error is 1.010454 (50 iterations in 0.05 seconds)
## Iteration 400: error is 0.945363 (50 iterations in 0.05 seconds)
## Iteration 450: error is 0.917389 (50 iterations in 0.05 seconds)
## Iteration 500: error is 0.902785 (50 iterations in 0.05 seconds)
## Iteration 550: error is 0.894018 (50 iterations in 0.05 seconds)
## Iteration 600: error is 0.888088 (50 iterations in 0.05 seconds)
## Iteration 650: error is 0.883727 (50 iterations in 0.05 seconds)
## Iteration 700: error is 0.880320 (50 iterations in 0.05 seconds)
## Iteration 750: error is 0.877578 (50 iterations in 0.05 seconds)
## Iteration 800: error is 0.875147 (50 iterations in 0.05 seconds)
## Iteration 850: error is 0.873129 (50 iterations in 0.05 seconds)
## Iteration 900: error is 0.871503 (50 iterations in 0.05 seconds)
## Iteration 950: error is 0.870060 (50 iterations in 0.05 seconds)
## Iteration 1000: error is 0.868780 (50 iterations in 0.05 seconds)
## Fitting performed in 0.99 seconds.mets.info.tsne <- cbind(tsne$Y, mets.info)
colnames(mets.info.tsne)[1] <- "tsne1"
colnames(mets.info.tsne)[2] <- "tsne2"
ggplot(mets.info.tsne, aes(x=tsne1, y=tsne2, color=Karyotype)) + geom_point() + theme_bw() 
tsne <- Rtsne(mets, pca=F, verbose=T, perplexity=100, theta=0)## Read the 415 x 174 data matrix successfully!
## Using no_dims = 2, perplexity = 100.000000, and theta = 0.000000
## Computing input similarities...
## Symmetrizing...
## Done in 0.02 seconds!
## Learning embedding...
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## Fitting performed in 0.97 seconds.mets.info.tsne <- cbind(tsne$Y, mets.info)
colnames(mets.info.tsne)[1] <- "tsne1"
colnames(mets.info.tsne)[2] <- "tsne2"
ggplot(mets.info.tsne, aes(x=tsne1, y=tsne2, color=Karyotype)) + geom_point() + theme_bw() 
UMAP: Uniform Manifold Approximation and Projection
We will use UMAP to plot the data and explore sample information
#Iris data
u <- umap(iris.mat)
iris.info.umap <- cbind(u$layout, iris)
colnames(iris.info.umap)[1] <- "UMAP1"
colnames(iris.info.umap)[2] <- "UMAP2"
ggplot(iris.info.umap, aes(x=UMAP1, y=UMAP2, color=Species)) + geom_point() + theme_bw() 
#HTP data
u <- umap(mets)
mets.info.umap <- cbind(u$layout, mets.info)
colnames(mets.info.umap)[1] <- "UMAP1"
colnames(mets.info.umap)[2] <- "UMAP2"
ggplot(mets.info.umap, aes(x=UMAP1, y=UMAP2, color=Karyotype)) + geom_point() + theme_bw() 
# to explore the parameters in UMAP, you can see the default values and adjust in the function
umap.defaults
u <- umap(mets, n_neighbors=5)
mets.info.umap <- cbind(u$layout, mets.info)
colnames(mets.info.umap)[1] <- "UMAP1"
colnames(mets.info.umap)[2] <- "UMAP2"
ggplot(mets.info.umap, aes(x=UMAP1, y=UMAP2, color=Karyotype)) + geom_point() + theme_bw() 
Session Information
sessionInfo()## R version 4.3.3 (2024-02-29)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Sonoma 14.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: America/Denver
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] factoextra_1.0.7 RCurl_1.98-1.14 limma_3.58.1 umap_0.2.10.0
## [5] Rtsne_0.17 ggfortify_0.4.17 ggplot2_3.5.1
##
## loaded via a namespace (and not attached):
## [1] gtable_0.3.5 xfun_0.45 bslib_0.7.0 ggrepel_0.9.5
## [5] rstatix_0.7.2 lattice_0.22-6 vctrs_0.6.5 tools_4.3.3
## [9] bitops_1.0-7 generics_0.1.3 tibble_3.2.1 fansi_1.0.6
## [13] highr_0.11 pkgconfig_2.0.3 Matrix_1.6-5 lifecycle_1.0.4
## [17] compiler_4.3.3 farver_2.1.2 stringr_1.5.1 statmod_1.5.0
## [21] munsell_0.5.1 carData_3.0-5 htmltools_0.5.8.1 sass_0.4.9
## [25] yaml_2.3.8 pillar_1.9.0 car_3.1-2 ggpubr_0.6.0
## [29] jquerylib_0.1.4 tidyr_1.3.1 openssl_2.2.0 cachem_1.1.0
## [33] abind_1.4-5 nlme_3.1-165 RSpectra_0.16-1 tidyselect_1.2.1
## [37] digest_0.6.35 stringi_1.8.4 dplyr_1.1.4 purrr_1.0.2
## [41] labeling_0.4.3 splines_4.3.3 fastmap_1.2.0 grid_4.3.3
## [45] colorspace_2.1-0 cli_3.6.2 magrittr_2.0.3 utf8_1.2.4
## [49] broom_1.0.6 withr_3.0.0 scales_1.3.0 backports_1.5.0
## [53] rmarkdown_2.27 reticulate_1.37.0 gridExtra_2.3 ggsignif_0.6.4
## [57] askpass_1.2.0 png_0.1-8 evaluate_0.24.0 knitr_1.47
## [61] mgcv_1.9-1 rlang_1.1.4 Rcpp_1.0.12 glue_1.7.0
## [65] jsonlite_1.8.8 R6_2.5.1